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y = cos ^(-1)((2x)/(1 +x^(2))),-1 lt x l...

`y = cos ^(-1)((2x)/(1 +x^(2))),-1 lt x lt1`. find dy/dx

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To find the derivative \( \frac{dy}{dx} \) for the function \( y = \cos^{-1}\left(\frac{2x}{1 + x^2}\right) \) in the interval \( -1 < x < 1 \), we will use the following steps: ### Step 1: Substitute \( x \) with \( \tan \theta \) Let \( x = \tan \theta \). Then, we can express \( \theta \) as: \[ \theta = \tan^{-1}(x) \] ...
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